The finite ridgelet transform for image representation

Minh N. Do, Martin Vetterli

Research output: Contribution to journalArticlepeer-review

Abstract

The ridgelet transform was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines. In this paper, we propose an orthonormal version of the ridgelet transform for discrete and finite-size images. Our construction uses the finite Radon transform (FRAT) as a building block. To overcome the periodization effect of a finite transform, we introduce a novel ordering of the FRAT coefficients. We also analyze the FRAT as a frame operator and derive the exact frame bounds. The resulting finite ridgelet transform (FRIT) is invertible, nonredundant and computed via fast algorithms. Furthermore, this construction leads to a family of directional and orthonormal bases for images. Numerical results show that the FRIT is more effective than the wavelet transform in approximating and denoising images with straight edges.

Original languageEnglish (US)
Pages (from-to)16-28
Number of pages13
JournalIEEE Transactions on Image Processing
Volume12
Issue number1
DOIs
StatePublished - Jan 2003

Keywords

  • Directional bases
  • Discrete transforms
  • Image denoising
  • Image representation
  • Nonlinear approximation
  • Radon transform
  • Ridgelets
  • Wavelets

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Software
  • Electrical and Electronic Engineering
  • Theoretical Computer Science

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